Solve 4m^4-100

$$4 m ^ { 4 } - 100$$

Factor

$$4\left(m^{2}-5\right)\left(m^{2}+5\right)$$

Solution Steps

Factor out 4.

$$4\left(m^{4}-25\right)$$

Consider m^{4}-25. Rewrite m^{4}-25 as \left(m^{2}\right)^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(m^{2}-5\right)\left(m^{2}+5\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: m^{2}-5,m^{2}+5.

$$4\left(m^{2}-5\right)\left(m^{2}+5\right)$$

Evaluate

$$4\left(m^{4}-25\right)$$